April weather can be unpredictible -- it can be nice or it can be dreadful, or all of the above and somewhere inbetween during your stay. Sometimes, you will find places just open for the spring in April, after Easter, in the countryside. You may find some tour offering less in that time, in Provence -- I encourage you to consider a car for at least a couple of days to maximize your trip. The driving is super easy in the villages and small towns of Provence. .
It is not necessary in Nice, where I have an apartment. You may see the hours on a rare place reduced but almost all business will be open in April (with the exception of the beach clubs and other relate summer businesses). January and sometimes November is when some restaurants close to take their holidays.